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Factor of iid Wiki
Welcome to the Factor of iid Wiki Wiki page for the factor-of-iid reading group at the Renyi Institute Budapest. Participants: edit this page freely. It is OK to reorganize and tidy things up if you like. Put your availability in the meeting times section. Meeting times Here is finally the doodle page to vote for the permanent times: http://doodle.com/auka6273awwhbvmg W 12:15, F 12:15? (with pizza?) NEXT MEETING: ''' ' --- W 16/4 12:15: Mustazee Rahman on FIID percolation with finite componenets. W 19/3 12:15: Viktor Harangi on factor of iid sets with finite components. F 14/3 12:15: ''Ágnes Backhausz on the equivalence of the tail triviality and the extremity of the Gibbs measure. W''' 13/3' '11: Ágnes Backhausz on the extremal Gibbs measures of the Ising model on the tree BlRuZa. F 28/2 12:15 Mustazee Rahman will continue. W 26/2 12:15: Mustazee Rahman on the slow mixing of the Glauber dynamics for the Ising model and on the Montanari paper GeMo. F 21/2 12:15, Miklós Abért on entropy, isomorphisms and sofic groups. W 19/2 12:15 Ágnes Backhausz will speak about mixing times of Glauber dynamics on trees (BKMP and MoSl in the list below) . F 14/2 12.15: Pizza! + Mustazee Rahman on the entropy method and/or f-invariant of Lewis Bowen Bo. T 2/11 12pm: Bálint Vető on the Karen Ball paper F 2/7 12pm: Máté Vizer will speak about Allan Sly's paper on Markov chain reconstruction in the Potts model (no. 2.). W 2/5 at 11am. Ágnes Backhausz will continue and present the proof of Theorem 1.3. in paper no. 5. in the list below. F 1/31 at 12am (Balint: how about 12pm=del? :-)) : Ágnes Backhausz will talk about Markov chain reconstruction on trees based on the paper no. 5. in the list below (Evans et al.). W 1/29 at 11am, 2nd floor lobby in Rényi Viktor Harangi will talk, topics to be announced. We will discuss some organizational issues. Gergő: Usually not good: Monday 16-18 (seminar in Renyi) Tuesday 8-10, Wednesday 10-12, sometimes Thursday 16-17 (BME Stochastics seminar), and Friday 8-12. Category:Browse Papers to read / topics to consider *Ly R. Lyons, '''Factors of IID on Trees. http://arxiv.org/abs/1401.4197 *Ba K. Ball, Factors of i.i.d. processes with nonamenable group actions. http://www.ima.umn.edu/~kball/factor.pdf review *Bo L. Bowen, A measure-conjugacy invariant for free group actions. http://arxiv.org/abs/0802.4294 *LyNa R. Lyons, F. Nazarov, Perfect Matchings as IID Factors on Non-Amenable Groups. http://arxiv.org/abs/0911.0092 *GaSu D. Gamarnik, M. Sudan, Limits of local algorithms over sparse random graphs. http://arxiv.org/abs/1304.1831 *RaVi M. Rahman, B. Virág, Local algorithms for independent sets are half-optimal.http://arxiv.org/abs/1402.0485 *ÁBB Á. Backhausz, B. Szegedy, B. Virág, Ramanujan graphings and correlation decay in local algorithms. http://arxiv.org/abs/1305.6784 *LyTh R. Lyons, A. Thom, Invariant Coupling of Determinantal Measures on Sofic Groups. http://arxiv.org/abs/1402.0969 *GaSu14 D. Gamarnik. M. Sudan, Performance of the Survey Propagation-guided decimation algorithm for the random NAE-K-SAT problem. http://arxiv.org/abs/1402.0052 *HaJoLy O. Haggstrom, J. Jonasson, R. Lyons,' ''''Coupling and Bernoullicity in random-cluster and Potts models. 'http://arxiv.org/abs/math/0104174v2' Glauber dynamics and Gibbs measures: *Ly1989 R. Lyons, The Ising model and percolation on trees and tree-like graphs. https://projecteuclid.org/download/pdf_1/euclid.cmp/1104179469 uniqueness of the Gibbs measure for theta>1/(d-1) *BlRuZa P. M. Bleher, J. Ruiz, V. A. Zagrebnov. On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice. http://link.springer.com/article/10.1007%2FBF02179399 extremal Gibbs measures for 1/(d-1)<1/sqrt(d-1) *BKMP N. Berger, C. Kenyon, E. Mossel, Y. Peres: Glauber dynamics on trees and hyperbolic graphs. http://link.springer.com/article/10.1007%2Fs00440-004-0369-4 *MoSl E. Mossel, A. Sly: Exact thresholds for Ising-Gibbs samplers on general graphs. http://arxiv.org/abs/0903.2906[fast mixing for theta<1/sqrt(d-1)] *DeMo1 A. Dembo, A. Montanari, Ising models on locally tree-like graphs. http://arxiv.org/abs/0804.4726 [slow mixing for theta>1/(d-1)] *GeMo A. Gerschenfeld, A. Montanari, Reconstruction for models on random graphs. http://arxiv.org/abs/0704.3293'[slow mixing' for theta>1/(d-1)] *DeMo2 A. Dembo, A. Montanari, Gibbs measures and phase transitions on sparse random graphs. http://projecteuclid.org/download/pdfview_1/euclid.bjps/1271770268 On reconstruction for Ising and Potts model (~ recommended by Gábor, but written here by Ági): #Christian Borgs, Jennifer Chayes, Elchanan Mossel, Sebastien Roch: The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels, http://arxiv.org/pdf/math/0604366v1 #Allan Sly: RECONSTRUCTION OF SYMMETRIC POTTS MODELS, http://arxiv.org/pdf/0811.1208.pdf #Svante Janson, Yuval Peres: ROBUST RECONSTRUCTION ON TREES IS DETERMINED BY THE SECOND EIGENVALUE, http://arxiv.org/pdf/math/0406447.pdf. #Robin Pemantle, Jeﬀrey E. Steif: Robust Phase Transitions for Heisenberg and Other Models on General Trees. http://arxiv.org/pdf/math/0404092v1 #Evans, Kenyon, Peres, Schulmann: Broadcasting on trees and the Ising model. http://projecteuclid.org/euclid.aoap/1019487349 Category:Browse Open questions 1. When is the symmetric 2-state Markov chain with uniform stationary distribution a factor of iid on T_d? 1a. Does some version of the entropy bound ever beat the correlaction decay bound? 1b. Is there monotonicity (i.e. is there a critical treshold in this problem)? 2. Does d-bar convergence imply that there exist factor maps that converge? 3. Is there a nontrivial process for which the entropy bound is sharp? 3a. Is the entropy bound sharp for the max-cut problem on T_d with asymptotically large d? 4) Several problems about Gaussian wave functions (GWF) on unimodular graphs: *For what eigenvalues of a unimodular graph does GWFs exists? *What are the best or general ways to construct GWFs? Two possibilities include spectral projection of IID Gaussians or to use eigenvectors of a sofic approximation, if it exists. *When is a GWF a limit of FIID and when is it a FIID itself? *If GWFs do exist, are they uniquely determined in some sense? What are some general properties of GWF on unimodular graphs? What can be said of the covariance structure? *This is related to the previous question. Does the subspace of GWFs for an eigenvalue outside the point spectrum have zero Von Neumann dimension? Does the answer depend on amenabibily? *Can we work out these problems for a specific unimodular network, for example, Poisson-Galton-Watson trees or periodic trees? People who want to participate Gábor Pete, Ági Backhausz, László Tóth, Mate Vizer, Bálint Virág, Gabor Kun, Bálint Vető, Viktor Harangi, Gergő Kiss, Mustazee Rahman, Endre Szabó, Michał Kotowski Category:Browse